Impeller having a centrifugal fluid handling means having steadily curving vanes



April 29, 1969 MASUKICHI KONDO 3,440,969

IMPEIJLIER HAVING A CENTRIFUGAL FLUID HANDLING MEANS HAVING STEADILY CURVING VANES Filed June 19, 1968 Sheet of 6 Fig- 1. Relation between relative path and absolute path in an impeller- Fig. 2. A velocity triangle showing a VeIOCiiy of flow in an impeller.

A velocity triangle Composed of oints of Y and Y AY in radius.

INVENTOR MASUKlCl-ll KON DO April 29, 1969 M ASUKICHI KONDO 3,440,969

IMPELLER HAVING A CENTRIFUG'AL FLUID HANDLING MEANS HAVING STEADILY CURVING VANES Filed June 19, 1968 Sheet Z of 6 Fig. 4A. A diagram showing dHects 0; the single arc vane (the vane angle/3 increases from/3F)? to flz= 25) Fig. 48. A diagram showing defects of the single arc vane (the vane angle/3 decreases from p.=25 toflz=l7) INVENTOR MASUKICH] KONDO ATTORNEYS April 29, 1969 MASUKICHI KONDO IMPELLER HAVING A CENTRIF'UGAL FLUID HANDLING MEANS HAVING STEADILY CURVING VANES 3 Filed June 19, 1968 Sheet of 6 A diagram showing defects of a Vane composed of two arcs Fig. 5.

(the vane angle/3 increases from/i=i'7' fa fl -ZS) A diagram illustrating the drawing methodof the vane Fig. 6.

deciding the vane profile by i'he eguation tan fi=Ar/YA9.

INVENTOR MASUKICHI KONDO BY A 7 dew Z fixed ATTORNEYS April 29, 1969 MASUKICHI KONDO 3,440,969

IMPELLER HAVING A CENTRIFUGAL FLUID HANDLING MEANS HAVING STEADILY CURVING VANES Filed June 19, 1968 Sheet of 6 Fig. -7. A diagram illustrating the radius of curvaturef. 0} a vane Fig. 8 A diagram illustrating differences between the arc vanes and the vane according to the present invention. (fhe vane angle [3 increases r0m/3i= I?" to fiz= 5 INVEN TOR MASU KlCl-Il KON DO ATTORNEYS April 29, 1969 MASUKICHI KONDO 3,440,969

IMPELLER HAVING A CENTRIFUGAL FLUID HANDLING MEANS HAVING STEADILY CURVING VANES 5 Filed June 19. 1968 Sheet of 6 Fig. q. A diagram illustrating difierences between i'he single arc vane and the vane according to the resent invention. (the vane angle/3 decreases from p.=25tofiz=l7') F g. 10! A diagram showing the errors 0 vane-profile drawn b the eguation AYx+l=fanflz Y1 A9 INVENTOR MASUKICHI KONDO A ril 29, 1969 MASUKICHI KONDO 3,440,969

IMPELLER HAVING A CENTRIFUGAL FLUID HANDLING MEANS HAVING STEADILY CURVING VANES Filed June 19, 1968 Sheet 6 of s Fig. 1!. A comparative diagram showing differences between the vane profiles according to the resent invention in casewhere INVENTOR MASUKIC H I KONDO BY 4 A ATTORNEYS United States Patent US. Cl. l03115 2 Claims ABSTRACT OF THE DISCLOSURE An impeller for a centrifugal fluid handling means. The impeller has vanes curving steadily and at a uniform rate from the outer periphery thereof to the inner periphery thereof in a smooth curve. The vanes have a curvature satisfying the condition:

wherein a the central angle between the origin of the vane at one of said peripheries and a point x along the vane;

fi =the vane angle at said point x;

B =the vane angle at the origin of the vane; and

The vane angle decreases or increases steadily at a uniform rate from the point of origin of the vane to the outer periphery.

This application is a continuation-in-part of application Ser. No. 530,712 filed Feb. 28, 1966, now abandoned.

This invention relates to a vane for an impeller for a pump, such as a centrifugal pump, a centrifugal blower, or the like, and for a centrifugal fluid driven device, such as a water turbine, a torque convertor, or the like.

It has been concluded that the best way to obtain the best energy transmission efliciency between a revolving impeller and the fluid being impelled is to harmonize the magnitude of the energy transmitted to the fluid from all portions of the vanes of the revolving impeller by causing the vane angle to change steadily at a uniform rate between the inlet and outlet.

The added force is proportional to the acceleration of the fluid obtained thereby. Therefore, the best way to improve the energy transmission efliciency is to have the circumferential acceleration a,=dv /dt acting on the fluid, e.g. water, passing through the space between the vanes harmonized for all portions of the vane.

The main factors which regulate the value a, are radial acceleration dv /dr and the progressive change dfi/dr of the vane angle ,6 along the vane.

Regulation of dv /dr can be readily achieved by varying the vane-width b. However, a method of determining dB/dr properly has not yet been established.

It is, therefore, an object of the present invention to improve the vane profile for achieving a reasonable progressivechange dfl/dr of the vane angle in order to improve the energy transmission efliciency between the vane and the fluid. This is accomplished by making the vane angle ,8 according to the formula B =B +(0 /m) or the formula B =fi (0, m) in order to obtain the best energy transmission efficiency by harmonizing the energy transmission between the vane and the fluid by harmonizing the acceleration a =a +a +a, +a,

The invention will be more fully understood from the 3,440,969 Patented Apr. 29, 1969 "ice following detailed description, taken together with the accompanying drawings, in which:

FIG. 1 is a diagram showing the relationship between the relative and absolute path of a fluid in an impeller;

FIG. 2 is a diagram of a velocity triangle showing the velocity relationships in the impeller;

FIGS. 3A and 3B are diagrams of velocity triangles at poirlits r and r-l-dr of the radius of the impeller, respective y;

FIG. 4A is a diagram showing the defects of a single arc vane where the outlet angle 5 is larger than the inlet angle [31;

FIG. 4B is a diagram similar to that of FIG. 4A where inlet angle ,8 is greater than outlet angle (3 FIG. 5 is a diagram showing the defects of a vane composed of two arcs where ,8 fi

FIG. 6 is a diagram illustrating a vane profile according to the equation v =tan fl v dfi;

FIG. 7 is a diagram showing the radius of curvature of a vane;

FIG. 8 is a diagram illustrating the differences between the arc vanes and the vane according to the present invention where {3 B FIG. 9 is a diagram similar to FIG. 8 where {3 fl FIG. 10 is a diagram showing the differences between a vane based upon successive calculations, as used in connection with FIG. 6, and a vane according to the present invention; and

FIG. 11 is a diagram showing the differences between vane profiles according to the present invention where 51 l 2 and I 1 B2- DEFINITIONS Throughout the specification and claims the following terms will have the meanings as set forth. Reference is made to FIGS. 1 and 2 for the vector and locations of the points at which the various measurements or vectors are located.

r=Radius at an arbitrary point on an impeller 0=Central angle subtended by a vane (see FIG. 1) w=Angular velocity of the impeller (rad./ sec.) w=Angular velocity of fluid passing through between the v Radial component of the velocity V=V i LX =Radius of curvature of the absolute path of fluid flow a zTangential acceleration of the fluid in the absolute path-dv/dt a =Normal acceleration acting of the fluid in the absolute path=v p a=Resultant of acceleration 11, and a a,,:Circumferential component of vector 3 a =Radial component of vector 11 do a-dtn/dlcos 1).-E sm 0.

( 1) Energy transmitting action between the vane and the fluid In order to transmit the energy .from the vane to, the fluid or vice versa, it is necessary to give an acceleration a, to the liquid in the circumferential direction in which the revolving force F acts (FIG. 1). In carrying out pumping, the circumferential acceleration is given to the fluid by the vane and the'fluid is displaced outwards. In driving an impeller, e.g. a water turbine, the circumferential acceleration of the fluid passing through the wheels from the outside to the inside causes a rotational force to be applied to the wheel.

Summarizing, the energy transmitted is proportional to the circumferential acceleration a of the fluid.

('2) A velocity triangle for the flow of the fluid inside the impeller The following illustration of a velocity triangle for the fluid inside the impeller will be given in order to aid in the explanation of the present invention. Let the peripheral velocity of the vane at an arbitrary point S on the impeller be vector u, the angle of the vane be e and the relative velocity of the fluid be vector w. The vector representing the absolute velocity v of the fluid is a diagonal v of a parallelogram having u and w as its two sides (see FIG. 1). The relative path of the fluid is S and its absolute path is S S' (see FIG. 1).

It is convenient to represent the relation of u, v and w as a velocity triangle as shown in FIG. 2, which is a conventional way of representing these quantities.

(3) Factors causing circumferential acceleration a, of the fluid In order to harmonize the energy to be transmitted at every point on the vane, it is only necessary to harmonize a In order to harmonize a the factors constituting a, must be studied. The following four elements together make up a, (see FIGS. 2 and 3).

(A) An acceleration a,, caused by the increase of u from u=rw to u: (r,+dr)w owing to the radial displacement of fluid at constant velocity (see FIGS. 3A and 3B).

(B) An acceleration a,, caused by the increase of a,, from a =rw' to a (l+dr)w' owing to the radial displacement of fluid at constant velocity (see FIG 2).

aa-a=-cot B% v, not 5% (3) (D) An acceleration a., caused by d B/dr, the variation of angle B. If the angle [3 is increased, v cot ,3 in

FIG. 2 is decreased, and no is increased correspondingly.

d (cot l3) d (cot 6) dr 2 2 dB 01B a94-'Ur dt -vr v 00sec B -w I? The combined acceleration a along the circumferential direction is represented by the following equation:

The above Equation 5 is a new theoretical equation according to the invention.

The following equation, which is the equation given for quantity a is a theoretical equation in which a numerical solution is impossible because p and dv/dt are unknown values.

The equation with values p and 'dv/dt can be changed into an equation which can be numerically solved as follows:

The value a, can thus be calculated by this theoretical equation. The equation with values p and dv/dt is made equal to an equation which can be numerically solved bv making Equation 6 equal to Equation 5.

The next problem to be solved is to establish a method of forming the vane in which the vane angle is steadilv increased or steadily decreased at a uniform rate.

(4) Defects of existing vane-forms. There is at present no system of forming a vane so as to achieve a uniform variation of dB/dr from [3 to 5 according to a prearranged plan. Most of the vanes in practical use have vanes in the shape of a circular arc. An analysis will be made of an impeller having a ratio r /r =2.63, in which the vane angle 5 increases from fl =l7 to ,B =25, and a similar impeller in which the angle it decreases from 5 :25 to :17".

(A) Single arc vanes in which the vane has ti fl and B B are shown in FIGS. 4A and 4B, respectively. In such a single arc vane, the central angle between the center 0 of the impeller axis and the center 0' of the arc is equal to vane-angle 3. Both where fl fi and where [3 fi the maximum value of angle ,6 exists at some point between fl and ,6 as shown in FIG. 4A and FIG. 4B. A steady increase or decrease of the angle 9 does not occur, as is clearly shown in FIGS. 4A or 4B.

(B) A vane formed by connecting two arcs is used in an attempt to relieve the defects 'in the shape of a single arc vane. FIG. 5 shows an example of the vane formed by two arcs having their centers at O and 0", respectively, and in which fi =l7, an intermediate angle fi =22 and fi =25. Angles fi having a value greater than the end angles on the arcs exist both between ,8 and {3 and between 5 and 8 Although maximum values of the angle 5 are less than the case of the single arc vane, the frequency of the increase and decrease of the vane angle is doubled. Thus, a two are vane does not provide steady increase of the vane angle any more than does a single arc vane.

(C) There has been proposed a system of determining the vane-form by deciding on a vane-angle and then making successive calculations. Such a vane form is shown in FIG. 6. A component in the circumferential direction along a minute distance As on the vane is r A and a component in the radial direction is Ar. The points I), c and d in FIG. 6 are determined successively by calculating Ar for every central angle A0 by means of the equation:

and the vane-profile is constructed using Ar to establish a point on the radius'at A6. In the above equation, A0 is an angle measured in radians.

However, Equation 8 is correct only for the mean position of the points x and x-l-l. The correct equation is as follows:

fl and r in Equation 8' are numerical values which can be determined only after calculation is made, and are unknown value. Equation 8' therefore is an equation which is impossible to solve numerically.

Moreover, the above mentioned errors are accumulated when values are calculated by means of Equation 8 used in place of Equation 8.

The following example is calculated by means of Equation 8. It is desirable that the angle 6 increase 1 for every 18 change of the central angle A6, starting from [3 =17 to 13 =25 at the point r =2.63r

The calculated values, ,8, r and r /r for every 18 of A6 are shown in Table 1.

TABLE l.-TABLE OF VANE DIMENSIONS CALCULATED SUCOESSIVELY BY MEANS OF THE EQUATION 8 6 (deg.) 18 36 54 72 90 108 126 144 162 {3 (deg.) 17 18 19 20 21 22 23 24 25 26 r, (mm. 34. 0 37. 3 41. 1 45. 50. 7 56. 8 64. 1 72. 6 82. 7 94. 8 r lri 1. 00 1. 1. 21 1. 34 1. 49 1. 67 1. 88 2. 13 2. 43 2. 78

AB/AG constant. The following equation is established: AQ AB= A Z A1 A0 0 0 Where Ari/AB is denoted by m, the value In designates a multiple of the variation of angle A0 of central angle 6 corresponding to a variation of Afl=fi -fl =l, so that the following equation is obtained:

Since A0 /Afl =A0 /A/3 =A0 /A,8 :m, the following equation is obtained:

Z(A0 +A0 A9,.) 0 =m Z(ABI+AB2+ BX) Bx Bl Therefore, when the angle ,8 steadily increases (i.e. m 0) the following equation is obtainedz When the angle [3 steadily decreases (i.e. m: 0), the following equation is obtained:

The following equations are equations establishing vaneforms which satisfy the foregoing Equations 9-A and 9-B:

The following equations are obtained by varying the above Equations l0-A and l0B:

-tan 6 m A6 The following equations are obtained by integrating the above Equations 1l-A and ll-B:

x ATX x & it. I a. tan m) (l -B) r and 0 are variables. As d(log cos )d=tan a the following equations are obtained by integrating the above Equations l2-A and l2B:

log r =+m log {cos (ti -g Since AS is the product of mo and sec [3 (FIG. 7), the quantity AS can also be represented as follows:

AS=rA0 sec B=r sec ,8 d9 (15) From the Equations 14 and 15, the following equation can be obtained as a general solution for the value p.

=r sec [3 dG/dqb .(16)

To determine the value of p where angle 5 is varied as in the Equations 9-A and 9B, from the triangle RPS in FIG. 7, the following equation can be drawn:

(ll-A) a=p+A0 (17) The angle 6 can also be represented as follows (see FIG. 7):

A0 ?i) s-B) By using the Equations 17 and 18:

A6 T; (IQ-A) A6 TE (19-13 Substituting the Equation 19 in the Equation 16:

The value p is proportional to the product of the radius and sec B. Since radius r and vane-angle B at each point on the vane are different respectively, the radium of curvature p differs at each adjacent point on the vane, and increases or decreases gradually.

The angle formed by line r and line p is equal to the angle ,8 (see FIG. 7). The angle B at each adjacent point on the vane is different from the angle at an adjacent point, as shown by the Equation 9-A or 9B. The center point of the radius of curvature for each point of the vane is thus different from that for the adjacent point and changes regularly.

In order to illustrate a practical embodiment of the vane of the present invention, calculations have been made for an impeller meeting the same conditions as that for which the calculations of Table 1 were made. Where the angle [3 increases gradually from B =17 to 5 :25", the relation between the angle [3 and the radius r is shown in Table 2, and the vane-profile is shown in FIG. 8.

In FIG. 8, the profiles of the vane shown in FIGS. 4A and 5 are shown in dotted lines for comparison.

TABLE 2.RELATION BETWEEN ANGLE B AND RADIUS 1 FOR A GRADUAL INCREASE OF ANGLE 9 (deg) O 18 36 54 72 90 108 126 144 13 (deg) 17 18 19 20 21 22 23 24 25 r (IDJIL) 34. 37. 4 41. 6 46. 6 52. 4 59. 3 67. 1 77. 89. 5 l'x/rl 1. 00 1. l. 22 1. 37 1. 54 1. 75 1. 98 2. 28 2. 63

TABLE 3.RELAIION BETWEEN ANGLE 6 AND RADIUS! FOR A GRADUAL DECREASE OF ANGLE 0 (deg) 0 18 30 54 72 90 108 126 144 19 (deg) 25 24 23 22 21 19 18 17 1 (111111.) 34. 0 39. 3 45. 0 51. 3 58. 0 65. 2 72. 8 81. 0 89. 5 r/rr 1. 00 1. l5 1. 32 1. 51 l. 71 1 91 2. l4 2. 38 2. 63

The vane-profile in accordance with Table 1, the values of which were obtained by the successive calculations, and the vane-profile in accordance with Table 2 according to the present invention, are compared in FIG. 10. The difierences in the profiles shows the errors produced by the successive calculation method using the Equation 8.

As shown in FIG. 10, the value r determined by the successive calculation method is smaller with a gradual increase of the angle [3 then the values corresponding to r when the vane-profile according to the present invention has a gradual increase of the angle [3.

When the vane-angle 5 increases gradually as well as when it decreases gradually, a uniform variation of d S/ dr from 5 to 5 at a predetermined ration r /r (2.63 is the example given in the present application) can be achieved only by the vane-profile of the present invention.

The difference between the vane-profile of the present invention in which the vane angle 5 increases gradually from ,B =17 to B =25 and that in which the vane angle ,3 decreases gradually from 3 =25 to [3 17 is shown in FIG. 11.

What is claimed is:

1. An impeller for a centrifugal fluid handling means, said impeller having vanes curving steadily and at a uniform rate from the outer periphery thereof to the inner periphery thereof in a smooth curve, said vanes having a curvature satisfying the condition fi =fl (0 /m) where- 1n:

6 =the central angle between the origin of the vane at one of said peripheries and a point x along the vane;

=the vane-angle at said point x; B =the vane angle at the origin of the vane; and I x 'fl1' 2. An impeller for a centrifugal fluid handling means, said impeller having vanes curving steadily and at a uniform rate from the outer periphery thereof to the inner periphery thereof in a smooth curve, said vanes having a curvature satisfying the condition p =,B +(0 /m) where- 1n:

0 =the central angle between the origin of the vane at one of said peripheries and a point x along the vane; B =the vane-angle at said point x; B =the vane-angle at the origin of the vane; and ms=0/fi fl References Cited UNITED STATES PATENTS 1,509,653 9/1924 Kaplan 103-115 963,378 7/1910 Lorenz 1031 15 1,906,180 4/1933 Rees 103-115 909,863 1/1909 Bowie 230--127 2,767,906 10/1956 Doyle 230134.45 3,226,085 12/1965 Bachl 1031 15 FOREIGN PATENTS 1,324 1863 Great Britain.

OTHER REFERENCES Cent. Pumps and Blowers by Austin H. Church, copya right 1944, 103-111B pages 19-20 and 118-128.

HENRY F. RADUAYO, Primary Examiner.

U.S. Cl. X.R. 29--156.8 

